Pith. sign in

REVIEW 3 major objections 4 minor 63 references

Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For biological ODE discovery, LLM agents are most useful as formalizers of biological knowledge, not as direct equation writers, and the paper shows that constraint-guided symbolic search recovers plausible mechanistic models where pure dat

desk verdict Solid agentic ODE-discovery pipeline with a load-bearing gap: the pretrained-formalizer ablation hits term F1 = 1.00 on extrapolation/discovery, so the 'reasoning' claim needs a memorization probe before it holds. read the letter →

arxiv 2607.13608 v1 pith:KQQFSRRA submitted 2026-07-15 cs.AI math.DS

David Krongauz , Arad Zulti , Eran Segal , Teddy Lazebnik This is my paper · ORCID
classification cs.AImath.DS
keywords agenticscientificdiscoverysymbolicregressionordinarydifferentialequationssystemsbiologylargelanguagemodelsmechanisticmodelingknowledge-guidedsearchequation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces MEDA, an agentic framework that combines large language models with constrained symbolic regression to discover ordinary differential equation (ODE) models of biological systems. The central claim is that LLM agents contribute most not by generating equations directly, but by translating incomplete biological knowledge into explicit variables, mechanistic constraints, candidate model structures, and critique criteria that guide symbolic search. Across retrieval, extrapolation, and open-ended discovery tasks, MEDA recovered correct state variables and strong structural skeletons even without fitting data. Ablations show that knowledge-guided formalization and constraints are load-bearing, while numerical fitting alone can preserve trajectory-compatible but biologically incorrect equations. This matters because biological modeling often lacks the symmetries and conservation laws of physics, leaving structural ambiguity as the main bottleneck.

What carries the argument

The central object is the Formalizer agent, which converts the Literature Surveyor's qualitative biological background into a machine-readable problem specification: admissible state variables, typed hard and soft constraints, candidate seed equations, protected core terms, and polynomial-degree limits. This specification then drives a constrained genetic search over sparse polynomial ODE systems, scored by a composite objective of constraint satisfaction, data fit (when available), and sparsity, with hard-constraint gating. The ground-truth equations are quarantined from all discovery agents and read only by the Evaluator after the blind search, isolating the reasoning chain from benchmark

What would settle it

Run a memorization probe: disable the literature-retrieval and formalization stages, prompt the LLM directly for the reference equations of the five extrapolation and two discovery systems, and check whether it emits the exact structures. If the pretrained model can produce the target equations (or near-equivalents), then the extrapolation and discovery results are at least partially explained by parametric recall, not by the agentic reasoning chain.

Watch

Extended reading notes

Core claim

The paper demonstrates that in biological ODE discovery, the bottleneck is structural ambiguity rather than coefficient fitting, and that literature-derived formalization is the load-bearing component of the pipeline. MEDA's pipeline—literature survey, formalization into typed constraints and seed equations, constrained genetic search over polynomial ODE libraries, and post-hoc critique—recovers correct state spaces and near-correct mechanistic skeletons across canonical retrieval, reasoning-based extrapolation, and discovery settings. The ablation study shows that removing literature retrieval and formalization (pure SINDy or data-driven formalization) sharply degrades plausibility and term

Load-bearing premise

The load-bearing premise is that the LLM's parametric knowledge and the retrieved literature do not already contain the exact target equations, especially for the 'reasoning-based extrapolation' and 'discovery' benchmark systems; if the pretrained model can reproduce these targets from memory, the results reflect retrieval rather than reasoning.

Editorial extensions

If this is right

  • Knowledge-guided formalization can substitute for data: in constraint-only mode, MEDA recovers correct mechanistic skeletons purely from literature-derived constraints and sparsity preference.
  • Data anchoring is not monotonic: adding trajectory fitting can introduce spurious high-degree terms and omit defining biological couplings, so numerical fit must be interpreted alongside mechanistic plausibility.
  • Removing the formalizer (e.g., pure SINDy or data-only formalization) sharply degrades term precision and biological plausibility, confirming that the mechanistic prior is the load-bearing component.
  • Robustness to measurement noise and sparse sampling is high for well-constrained tasks, with degradation mainly reflecting reduced precision rather than loss of the true mechanism; the harder bottleneck is loss of mechanistically coupled latent variables.
  • The auditable artifact chain (literature review, constraints, seeds, diagnostics, critique) makes each discovered model inspectable, supporting a view of automated discovery as an explicit chain of mechanistic reasoning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's extrapolation and discovery results may overstate reasoning if the LLM's pretrained knowledge already contains the 'designed for this study' target equations; a memorization probe (e.g., generating targets after the model's knowledge cutoff, or testing with randomized variants) would separate retrieval from genuine extrapolation.
  • The polynomial-only search grammar excludes Hill kinetics, saturating functional responses, and delays common in biology; the formalizer-driven approach suggests these could be encoded as typed constraint templates rather than library extensions.
  • The expert plausibility score, while averaged across five biomathematicians, is subjective and could be complemented by automated mechanistic consistency checks that verify sign patterns and coupling structures against the constraint set.
  • MEDA's design implies a shifted role for human modelers: rather than proposing equations, they oversee and critique an explicit, revisable chain of assumptions—an approach adaptable to other fields with qualitative, distributed prior knowledge.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents MEDA, an LLM-agentic framework for discovering ODE models of biological systems. MEDA uses a Literature Surveyor, Formalizer, Runner (constrained symbolic regression), and evaluative agents to produce human-auditable artifacts: literature review, typed constraints, seed equations, and final candidate ODEs. It is evaluated on three benchmark tiers—information retrieval (standard models), reasoning-based extrapolation (variants designed for the study), and open-ended discovery (expert-defined targets)—in both constraints-only and data-anchored modes. The main reported findings are that MEDA recovers correct state variables and strong term-level structure in IR/EX tasks, that data fitting is not monotonic and can hurt mechanistic correctness, and that ablation results show knowledge-guided formalization is the load-bearing component of the pipeline.

Significance. If the central claim holds, the paper makes a useful contribution: it reframes LLM use in scientific discovery as formalization of incomplete biological knowledge into constraints and structures, rather than direct equation generation, and it provides an inspectable multi-artifact workflow. The paper is transparent about non-monotonic effects of data fitting, reports failures (e.g., FitzHugh–Nagumo adaptation, chronic wound), and ships code with a GitHub URL. The quarantine of ground-truth equations from discovery agents is a good experimental hygiene measure. However, the significance is conditional on establishing that the EX and DI results reflect reasoning rather than retrieval from the pretrained model, which is not currently demonstrated.

major comments (3)
  1. [§5.1, Table 2, Discussion] The central claim that EX/DI results demonstrate reasoning-based extrapolation and discovery is not established without a memorization probe. In Table 2, the 'pretrained formalizer' variant—which removes both literature retrieval and EDA/SINDy—achieves term F1 = 1.00 for IR, EX, and DI, so the only source of mechanism information is the LLM's parametric memory. The manuscript asserts in §5.1 that the EX equations 'were designed for this study and were not intended to be direct retrieval targets,' but no test is reported to verify that the pretrained model cannot reproduce them. Many of these systems (age-structured SIR, intraguild predation, Allee cooperation, FitzHugh–Nagumo adaptation) are close to existing published model families. A direct probe is needed: e.g., ask the formalizer/LLM to generate the ODEs from the same problem description without retrieval or search, or evaluate on s
  2. [Table 1, EX/SIR age-structured row] In the 'With data' EX SIR age-structured row, the predicted equation is shown as a single line 'dIY/dt = +IY SY + IO SY − IY / Same equation', while the ground truth is a six-compartment system. Variable F1, term F1, and inclusion are all reported as 1.00, which is internally inconsistent with the displayed prediction. Either the table is truncated or the evaluation protocol considers only a subset of the system; as presented, this row does not support the reported perfect scores. Please provide the complete predicted system and clarify the matching procedure.
  3. [§2 and §5.1 (Appendix)] The manuscript repeatedly refers to 'the Appendix' for full technical details and default implementation settings (e.g., 'Full technical details and default implementation settings are provided in the Appendix'), but no appendix is present in the submitted manuscript. Key reproducibility information is therefore missing: the genetic-programming objective, constraint-weighting scheme, sparsity penalty, polynomial-degree bound, SINDy screening threshold, LLM versions, prompt templates, and evaluation code. A journal submission must provide these details, either in the main text or in a clearly linked supplementary file, before the results can be independently reproduced.
minor comments (4)
  1. [§5.2 / Table 2] Plausibility scores are reported to three decimal places as averages of only five expert raters. No inter-rater agreement, confidence interval, or per-rater variance is given. Please report dispersion or justify the precision.
  2. [Table 3 / text] The text says that at 30% noise the age-structured SIR system is 'structurally correct but numerically unstable,' yet Table 3 reports term F1 = 1.00 at that noise level. Please clarify whether the score reflects structural correctness only and whether the instability affects the score.
  3. [Throughout] Minor typos and inconsistent terminology: 'metrices' (§5), 'Surveyer' vs 'Surveyor' (§2), and 'constraints-only mode' vs 'constraint-only mode'. Also, Table 1 uses 'Same equation' with no explanation.
  4. [§3 robustness paragraph] The 'fast-path' noise-robustness evaluation holds the formalizer fixed, so it does not test robustness of the literature/formalization stages to corrupted input. The paper acknowledges this, but the wording 'robustness of MEDA' may overstate the coverage; consider clarifying in the text.

Circularity Check

0 steps flagged · score 2.0 of 10

No derivation step reduces to its own input by construction; the missing memorization probe for EX/DI targets is a validity risk, not demonstrated circularity. Minor self-citations are not load-bearing.

full rationale

The paper's discovery pipeline is self-contained with respect to its stated design: the ground-truth equations are quarantined from all discovery agents (Fig. 1; Methods §5.1), and the LLM formalizer, literature surveyor, symbolic search, and numerical fitting are distinct stages. No fitted parameter is renamed as a prediction, and no target equation is defined in terms of the system's outputs. The IR setting is explicitly information retrieval, so recovering canonical models there is the intended task rather than a circularity. The EX and DI settings claim that the exact equations 'were designed for this study and were not intended to be direct retrieval targets' (Methods §5.1), but the paper does not probe whether the pretrained LLM memorized these equations. The pretrained-formalizer ablation in Table 2 reaches term F1 = 1.00 on EX and DI without literature retrieval or EDA, showing that parametric memory alone can supply the mechanism. If the targets appear in the LLM's training data, the 'reasoning-based extrapolation' and 'discovery' results would reduce to retrieval; however, this is an untested empirical possibility rather than a reduction that follows from the paper's own definitions or equations. The paper itself acknowledges that 'literature retrieval and pretrained biological knowledge can act as alternative sources of mechanistic prior' (Discussion), which is consistent with the formalizer being load-bearing even if some benchmarks are retrieval-like. The self-citations (e.g., refs. [40], [44], [45]) are used for background and for the TED-based expression score; they are not the load-bearing justification for the central claim, so they do not constitute circularity. Overall, the central derivation is independent; the memorization concern is a correctness/validity risk that should be addressed empirically but does not rise to a demonstrated circular step under the stated standard.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on assumptions about the search grammar, the trustworthiness of LLM/literature priors, the representativeness of simulated data, and the validity of expert plausibility scores. These are domain assumptions rather than standard mathematical axioms. The free parameters are the fitting/objective hyperparameters (constraint weights, sparsity preference, polynomial-degree limit) and the coefficient values fitted in data-anchored mode.

free parameters (3)
  • Constraint weights, sparsity preference, polynomial-degree limit in the search objective = Not specified in visible text (Appendix default settings)
    Hand-chosen hyperparameters controlling the trade-off between constraint satisfaction, data fit, and parsimony in the Runner; they shape all reported results.
  • Fitted ODE coefficients in data-anchored mode = Examples in Table 1: 0.23, −0.0001 (logistic); 0.80, −0.10, 0.10, −0.50 (Lotka–Volterra)
    Coefficients are fitted to simulated trajectories by the Runner; the paper's structural-recovery claims are supposed to be independent of exact values, but the data-anchored mode uses them as part of the objective.
  • SINDy screening threshold = Not stated in visible text
    Used by the Explorer to identify candidate terms in data-anchored mode (Figure 1); this threshold controls which terms enter the formalization.
assumptions (4)
  • domain assumption Polynomial ODE grammar of bounded degree is expressive enough for the benchmarked biological systems.
    The Runner searches only over sparse polynomial ODE systems (§2); all targets were selected to fit this grammar, and the Discussion concedes Hill kinetics, delays, thresholds, and stochastic effects are excluded.
  • domain assumption LLM/literature-derived constraints and seed equations are correct and sufficient guides to the target mechanisms.
    The Formalizer derives constraints from literature/LLM priors; the host–dual-pathogen case shows wrong family persists when constraint generation is wrong (Table 1), so this assumption is load-bearing.
  • domain assumption Simulated trajectories generated from the reference ODEs are a valid proxy for experimental biological data.
    Data-anchored mode supplies simulated trajectories (§5.1), yet the abstract calls them 'experimental data'; no real experimental time series are used.
  • domain assumption Expert plausibility scores from five biomathematicians provide a valid measure of biological coherence.
    Plausibility is the average of five expert ratings (Methods §5.2); it is subjective and not independently checked against data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System." pith.science (2026). https://pith.science/paper/KQQFSRRA

@misc{pith2026260713608,
  author       = {Pith},
  title        = {Pith review of: Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KQQFSRRA}},
  note         = {Machine review of arXiv:2607.13608}
}
read the original abstract

Automatic scientific discovery has long been a goal of computational scholars - a machine that can discover nature's secrets on its own, moving computational systems beyond data-fitting tools toward the generation and refinement of mechanistic models of the universe. Recent advances in symbolic regression (SR) and large-language-model (LLM)-based agents suggest that such systems can recover equations from data, incorporate domain priors, and automate parts of the research workflow. However, most existing approaches either focus on narrow equation-discovery benchmarks or broad end-to-end automation pipelines, while biological systems remain comparatively underexplored. Here, we introduce the MEDA system, an LLM- and SR-powered agentic framework for discovering ordinary-differential-equation (ODE) models of biological and biologically inspired dynamical systems. MEDA retrieves background knowledge, defines admissible variables, generates mechanistic constraints, proposes candidate ODEs, and fits and evaluates them. We evaluate it across canonical model retrieval, reasoning-based extrapolation to unseen variants, and open-ended discovery, with and without experimental data. Across these settings, MEDA recovered the correct state variables, achieved strong structural recovery in retrieval and extrapolation tasks, and produced biologically plausible discovery-oriented models. Ablation and robustness analyses show that knowledge-guided formalization and mechanistic constraints are load-bearing components, whereas numerical fitting alone can preserve trajectory-compatible but biologically incorrect equations.

Figures

Figures reproduced from arXiv: 2607.13608 by the authors.

Figure 1
Figure 1. Architecture of MEDA. Specialized agents (centre) each read a defined input artifact and write a defined output artifact (right) to a shared session directory. Solid arrows apply in both operating modes; green dashed arrows are active only in data-anchored mode, in which a supplied time series feeds the Explorer (EDA + SINDy screening) and the Runner. The ground-truth equations are quarantined from all discovery age… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 7 linked inside Pith

  1. [1]

    Lu, C.et al.Towards end-to-end automation of ai research.Nature651, 914–919 (2026)

    2026

  2. [2]

    Sparkes, A.et al.Towards robot scientists for autonomous scientific discovery.Automated experimentation2, 1 (2010)

    2010

  3. [3]

    Lenat 1, D. B. Automated theory formation in mathematics.Automated Theorem Proving: After 25 Years: After 25 Years89, 287 (1984). 14

    1984

  4. [4]

    Langley, P.Scientific discovery: Computational explorations of the creative processes(MIT press, 1987)

    1987

  5. [5]

    & King, R

    Kramer, S., Cerrato, M., Brugger, J., Dˇ zeroski, S. & King, R. D. Automated scientific discovery: From equation discovery to autonomous discovery systems.arXiv preprint arXiv:2305.02251(2023)

    arXiv 2023

  6. [6]

    Xin, H., Kitchin, J. R. & Kulik, H. J. Towards agentic science for advancing scientific discovery.Nature Machine Intelligence7, 1373–1375 (2025)

    2025

  7. [7]

    Merchant, A.et al.Scaling deep learning for materials discovery.Nature624, 80–85 (2023)

    2023

  8. [8]

    A., Mahmud, A.et al.Exploring the role of large language models in the scientific method: From hypothesis to discovery.npj Artificial Intelligence1, 14 (2025)

    Zhang, Y., Khan, S. A., Mahmud, A.et al.Exploring the role of large language models in the scientific method: From hypothesis to discovery.npj Artificial Intelligence1, 14 (2025)

    2025

Show all 63 references
  1. [9]

    & Clune, J

    Faldor, M., Zhang, J., Cully, A. & Clune, J. Omni-epic: Open-endedness via models of human notions of interestingness with environments programmed in code. InInternational Conference on Learning Representations, vol. 2025, 85260–85385 (2025)

    2025

  2. [10]

    & Ulrich, K

    Girotra, K., Meincke, L., Terwiesch, C. & Ulrich, K. T. Ideas are dimes a dozen: Large language models for idea generation in innovation.Available at SSRN4526071(2023)

    2023

  3. [11]

    & Clune, J

    Hu, S., Lu, C. & Clune, J. Automated design of agentic systems. InInternational Con- ference on Learning Representations, vol. 2025, 21344–21377 (2025)

    2025

  4. [12]

    Vinuesa, R.et al.Decoding complexity through machine learning is redefining scientific discovery.Communications Physics9, 168 (2026)

    2026

  5. [13]

    & Crockett, M

    Messeri, L. & Crockett, M. The uncritical adoption of ai in science is alarming—we urgently need guard rails.Nature653, 675–676 (2026)

    2026

  6. [14]

    Ai research assistants are changing science.Nature651, 853 (2026)

    That, A. Ai research assistants are changing science.Nature651, 853 (2026)

    2026

  7. [15]

    arXiv preprint arXiv:2408.06292(2024)

    Lu, C.et al.The ai scientist: Towards fully automated open-ended scientific discovery. arXiv preprint arXiv:2408.06292(2024)

    2024 arXiv

  8. [16]

    Schmidgall, S.et al.Agent laboratory: Using llm agents as research assistants.arXiv preprint arXiv:2501.04227(2025)

    2025 arXiv

  9. [17]

    Narayanaswamy, C. S. Can we write a research paper using artificial intelligence?Journal of Oral and Maxillofacial Surgery81, 524–526 (2023)

    2023

  10. [18]

    & Yoon, J

    Song, Y., Song, Y., Pfister, T. & Yoon, J. Paperorchestra: A multi-agent framework for automated ai research paper writing.arXiv preprint arXiv:2604.05018(2026)

    2026 arXiv

  11. [19]

    Shojaee, P.et al.Llm-srbench: A new benchmark for scientific equation discovery with large language models.arXiv preprint arXiv:2504.10415(2025)

    2025 arXiv

  12. [20]

    Z., Georgievska, A

    Bideh, A. Z., Georgievska, A. & Gryak, J. Mdbench: Benchmarking data-driven methods for model discovery. InProceedings of the AAAI Conference on Artificial Intelligence, vol. 40, 19746–19754 (2026). 15

    2026

  13. [21]

    R., Lober, L., Previdelli, I

    Brum, B. R., Lober, L., Previdelli, I. & Rodrigues, F. A. Discovering equations from data: symbolic regression in dynamical systems.Journal of Physics: Complexity7, 012001 (2026)

    2026

  14. [22]

    Son, G.et al.When ai co-scientists fail: SPOT—a benchmark for automated verification of scientific research.arXiv preprint arXiv:2505.11855(2025)

    2025 arXiv

  15. [23]

    Nature Machine Intelligence1–14 (2026)

    Kumaran, D.et al.Competing biases underlie overconfidence and underconfidence in llms. Nature Machine Intelligence1–14 (2026)

    2026

  16. [24]

    & Reviriego, P

    Fu, T., Conde, J., Martinez, G., Grandury, M. & Reviriego, P. Multiple choice questions: Reasoning makes large language models (llms) more self-confident, specially when they are wrong.IEEE Intelligent Systems(2026)

    2026

  17. [25]

    & Treutlein, B

    Cahan, P. & Treutlein, B. A conversation with chatgpt on the role of computational systems biology in stem cell research.Stem cell reports18, 1–2 (2023)

    2023

  18. [26]

    M., Shivnaraine, R

    Ahmed, S. M., Shivnaraine, R. V. & Wu, J. C. Fda modernization act 2.0 paves the way to computational biology and clinical trials in a dish.Circulation148, 309–311 (2023)

    2023

  19. [27]

    Chen, V.et al.Applying interpretable machine learning in computational biology—pitfalls, recommendations and opportunities for new developments.Nature methods21, 1454–1461 (2024)

    2024

  20. [28]

    Guo, Z.et al.Diffusion models in bioinformatics and computational biology.Nature reviews bioengineering2, 136–154 (2024)

    2024

  21. [29]

    & Marchetti, L

    Giampiccolo, S., Reali, F., Fochesato, A., Iacca, G. & Marchetti, L. Robust parameter estimation and identifiability analysis with hybrid neural ordinary differential equations in computational biology.NPJ Systems Biology and Applications10, 139 (2024)

    2024

  22. [30]

    & Radulescu, O

    L¨ uders, C., Sturm, T. & Radulescu, O. Odebase: a repository of ode systems for systems biology.Bioinformatics Advances2, vbac027 (2022)

    2022

  23. [31]

    Vieira, L. S. & Laubenbacher, R. C. Computational models in systems biology: standards, dissemination, and best practices.Current opinion in biotechnology75, 102702 (2022)

    2022

  24. [32]

    & Chawla, S

    Makke, N. & Chawla, S. Interpretable scientific discovery with symbolic regression: A review.Artificial Intelligence Review57(2024)

    2024

  25. [33]

    & Lipson, H

    Schmidt, M. & Lipson, H. Distilling free-form natural laws from experimental data.Science 324, 81–85 (2009)

    2009

  26. [34]

    Wang, H.et al.Scientific discovery in the age of artificial intelligence.Nature620, 47–60 (2023)

    2023

  27. [35]

    E., Atiku, S

    Chigbu, U. E., Atiku, S. O. & Du Plessis, C. C. The science of literature reviews: Searching, identifying, selecting, and synthesising.Publications11, 2 (2023)

    2023

  28. [36]

    & Reuter, K

    Scheurer, C. & Reuter, K. Role of the human-in-the-loop in emerging self-driving labora- tories for heterogeneous catalysis.Nature Catalysis8, 13–19 (2025)

    2025

  29. [37]

    Kallmes, K. M.et al.Human-in-the-loop artificial intelligence system for systematic liter- ature review: Methods and validations for the autolit review software.Cochrane Evidence Synthesis and Methods3, e70059 (2025). 16

    2025

  30. [38]

    Lee, D. J.-L. & Macke, S. A human-in-the-loop perspective on automl: Milestones and the road ahead.IEEE Data Engineering Bulletin(2020)

    2020

  31. [39]

    Frontiers in Ecology and Evolution8, 530135 (2020)

    Cardoso, P.et al.Automated discovery of relationships, models, and principles in ecology. Frontiers in Ecology and Evolution8, 530135 (2020)

    2020

  32. [40]

    & Lazebnik, T

    Simon-Keren, L., Liberzon, A. & Lazebnik, T. A computational framework for physics- informed symbolic regression with straightforward integration of domain knowledge.Sci- entific Reports13, 1249 (2023)

    2023

  33. [41]

    L., Proctor, J

    Brunton, S. L., Proctor, J. L. & Kutz, J. N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proceedings of the National Academy of Sciences113, 3932–3937 (2016)

    2016

  34. [42]

    & Dˇ zeroski, S

    Brence, J., Todorovski, L. & Dˇ zeroski, S. Probabilistic grammars for equation discovery. Knowledge-Based Systems224, 107077 (2021)

    2021

  35. [43]

    Shojaee, P., Meidani, K., Gupta, S., Farimani, A. B. & Reddy, C. K. LLM-SR: Scientific equation discovery via programming with large language models. InInternational Con- ference on Learning Representations (ICLR)(2025). URLhttps://openreview.net/ forum?id=m2nmp8P5in

    2025

  36. [44]

    & Lazebnik, T

    Taskin, B., Xie, W. & Lazebnik, T. Knowledge integration for physics-informed symbolic regression using pre-trained large language models.Scientific Reports(2026)

    2026

  37. [45]

    & Lazebnik, T

    Shmuel, A., Koren, N., Glickman, O. & Lazebnik, T. Interpretable knowledge distillation via symbolic regression for feedforward neural networks.Neural Computing and Applica- tions38, 243 (2026)

    2026

  38. [46]

    & Shen, L

    Zhang, X., Xu, L., Lu, J., Zhang, Z. & Shen, L. Physics-knowledge-integrated neural net- work for quantum transport prediction of field-effect transistors.Physical Review Applied 23, 034066 (2025)

    2025

  39. [47]

    & Tegmark, M

    Udrescu, S.-M. & Tegmark, M. Ai feynman: A physics-inspired method for symbolic regression.Science advances6, eaay2631 (2020)

    2020

  40. [48]

    & Babuˇ ska, R

    Kubal ´ ık, J., Derner, E. & Babuˇ ska, R. Multi-objective symbolic regression for physics- aware dynamic modeling.Expert Systems with Applications182, 115210 (2021)

    2021

  41. [49]

    & Wang, Z

    Lu, Q., Ren, J. & Wang, Z. Using genetic programming with prior formula knowledge to solve symbolic regression problem.Computational intelligence and neuroscience2016, 1021378 (2016)

    2016

  42. [50]

    O., Burlacu, B., Haider, C

    Kronberger, G., de Fran¸ ca, F. O., Burlacu, B., Haider, C. & Kommenda, M. Shape- constrained symbolic regression—improving extrapolation with prior knowledge.Evolu- tionary computation30, 75–98 (2022)

    2022

  43. [51]

    D., Nacion, F

    Fox, C., Tran, N. D., Nacion, F. N., Sharlin, S. & Josephson, T. R. Incorporating back- ground knowledge in symbolic regression using a computer algebra system.Machine Learn- ing: Science and Technology5, 025057 (2024)

    2024

  44. [52]

    InGenetic programming theory and practice XVII, 79–99 (Springer, 2020)

    Kammerer, L.et al.Symbolic regression by exhaustive search: Reducing the search space using syntactical constraints and efficient semantic structure deduplication. InGenetic programming theory and practice XVII, 79–99 (Springer, 2020). 17

    2020

  45. [53]

    A.et al.Delay differential equations and applications to biology (2021)

    Rihan, F. A.et al.Delay differential equations and applications to biology (2021)

    2021

  46. [54]

    & Rotariu, M

    Ilea, M., Turnea, M. & Rotariu, M. Ordinary differential equations with applications in molecular biology.The Medical-Surgical Journal116, 347–352 (2012)

    2012

  47. [55]

    & Wedelin, D

    Gennemark, P. & Wedelin, D. Efficient algorithms for ordinary differential equation model identification of biological systems.IET Systems Biology1, 120–129 (2007)

    2007

  48. [56]

    & MacLean, A

    Wu, X., McDermott, M. & MacLean, A. L. Data-driven model discovery and model selection for noisy biological systems.PLOS Computational Biology21, e1012762 (2025)

    2025

  49. [57]

    & Carvalho, R

    Egan, K., Li, W. & Carvalho, R. Automatically discovering ordinary differential equations from data with sparse regression.Communications Physics7, 20 (2024)

    2024

  50. [58]

    Jiang, Y.-X.et al.Modeling and prediction of the transmission dynamics of covid-19 based on the sindy-lm method.Nonlinear Dynamics105, 2775–2794 (2021)

    2021

  51. [59]

    L., Proctor, J

    Brunton, S. L., Proctor, J. L. & Kutz, J. N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proceedings of the national academy of sciences113, 3932–3937 (2016)

    2016

  52. [60]

    N.et al.Universally sloppy parameter sensitivities in systems biology models.PLOS Computational Biology3, e189 (2007)

    Gutenkunst, R. N.et al.Universally sloppy parameter sensitivities in systems biology models.PLOS Computational Biology3, e189 (2007)

    2007

  53. [61]

    Raue, A.et al.Structural and practical identifiability analysis of partially observed dy- namical models by exploiting the profile likelihood.Bioinformatics25, 1923–1929 (2009)

    1923

  54. [62]

    Champion, K., Lusch, B., Kutz, J. N. & Brunton, S. L. Data-driven discovery of coor- dinates and governing equations.Proceedings of the National Academy of Sciences116, 22445–22451 (2019)

    2019

  55. [63]

    Rackauckas, C.et al.Universal differential equations for scientific machine learning.arXiv preprint arXiv:2001.04385(2020).2001.04385. 18

    2001 arXiv

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.